The minimum energy required to launch a satellite of mass m from the surface of earth of radius R in a cirulcar orbit at an altitude 2R is (mass of earth is M)
The correct option is D.
Energy of the satellite on the surface of earth is only the potential energy given by.
Ei=−GmMR
The energy of satellite at a distance (2R + R) = 3R from center of earth is both potential as well as kinetic. Hence the total energy is given by,
Ef=−GmM2(3R)=−GMm6R
∴ Energy required to launch the satellite is
E = Ef−Ei=−GMm6R−(−GmMR)=5GMm6R.